American Invitational Mathematics Examination
The American Invitational Mathematics Examination (AIME) is the second exam in the series of exams used to challenge bright students on the path toward choosing the team that represents the United States at the International Mathematics Olympiad (IMO). While most AIME participants are high school students, some bright middle school students also qualify each year.
High scoring AIME students are invited to take the prestigeous United States of America Mathematics Olympiad (USAMO).
The AIME is administered by the American Mathematics Competitions (AMC). Art of Problem Solving (AoPS) is a proud sponsor of the AMC!
Contents
Format
The AIME is a 15 question, 3 hour exam taken by high scorers on the AMC 10, AMC 12, and USAMTS competitions. Qualification through USAMTS only is rare, however. Each answer is an integer from 0 to 999, making guessing pretty much futile. Wrong answers receive no credit, while correct answers receive one point of credit, making the maximum score 15. Problems generally increase in difficulty as the exam progresses - the first few questions are generally AMC12 level, while the later questions become extremely difficult in comparison. Calculators are not permitted.
Curriculum
The AIME tests mathematical problem solving with arithmetic, algebra, counting, geometry, number theory, and probability and other secondary school math topics. Problems usually require either very creative use of secondary school curriculum, or an understanding as to how different areas of math can be used together to investigate and solve a problem.
Resources
Links
- AMC homepage and their AIME page
- AIME Problems and Solutions -- A community effort to provide solutions to all AIME problems from which students can learn.
- The AoPS AIME guide.
- AMC Forum for discussion of the AMC and problems from AMC and AIME exams.
- The AoPS Contest Archive includes problems and solutions from past AMC and AIME exams.
- Mock AIME exams by AoPSers -- A wealth of secondary practice materials.
Recommended reading
- Problem and solution books for past AMC exams. One of these books also includes numerous past AIMEs and solutions.
- Introduction to Counting & Probability by Dr. David Patrick is recommended for students who qualify for the AIME, but feel they lag behind in their understanding of basic combinatorics and probability relative to their other areas of math. Information
- Introduction to Geometry by Richard Rusczyk. Information
- The Art of Problem Solving Volume II by Sandor Lehoczky and Richard Rusczyk. Information.
AIME Preparation Classes
- AoPS hosts an online school teaching introductory classes in topics covered by the AIME as well as AIME preparation classes.
- AoPS holds many free Math Jams, some of which are devoted to discussing problems on the AIME. Math Jam Schedule
